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(a) Use the formula of Exercise 18 to show that$$ F = (\rho g \bar{x}) A $$where $ \bar{x} $ is the x-coordinate of the centroid of the plate and $ A $ is its area. This equation shows that the hydrostatic force against a vertical plane region is the same as if the region were horizontal at the depth of the centroid of the region.(b) Use the result of part (a) to give another solution to Exercise 10.

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Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 3

Applications to Physics and Engineering

Applications of Integration

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

08:16

In Exercises $35-38,$ find…

10:47

04:17

Consider a plate having un…

08:34

09:28

In Exercises $18,$ find th…

10:39

08:14

03:35

In Exercises $37-40,$ let …

07:45

in this problem where? As to show that eh? Physicals wrote OMG have central mass types area and arrest to use. Um, the question for us as in trouble for me to be row time G tent that times with times being infinite dismal height You know that central mess Thanks for Is he going to inter Going to be x times w x The X divided by inter go a to be doubly x the x l s assume that we have an object or with or this is the X A direction and we're with off this object changes is a function of X and it was said that we're interested in this infinite, dismal sit trip an area off that that area would be w X times dx. And if you were to find a total area off this object, we would need to integrate this from a or A to B. So this is the area that combining these two. We see that then the function in the denominator is actually the area. It means that inter girl from A to B x deadly x d x is in confident. Expert are times area. Okay, you know that force is equal to internal A to B Road times, g times, X times definitely x t x, and we know that ruin. Gee, they're independent off X or D x so we can just take those outside in Trickle. I write this one as wrote OMG a to b x, w x e x and here we found W X DX to be eagles accepts export times. So let's just plugged it in and then right to force as rotund G times. Expert Time's a now important beat, whereas to use this expression so F is equal to row times G times export time site and apply it in to the exercise or for the object in exercise. 10. Now central mess off. This object is here, and the that off. The century would be the distance from the surface to this point, and that would be using this triangle that would be a over skirted off, too. So we didn't know that pressure is Road 10 g time step and that is road times G times. What is that? There's a function of a that is a over skirt of two, and you know that force is equal to pressure times, area and worried. The area for this square is a squared. So then the force would be road 10 g times a over skirted of two multiplied by area, which is a squared. So that would be row G. A cube. Delighted, skirted off, too. We know that row is 1000 for water in the sun. Unit G is 9.8. A cute deal I find scurried off to that would be than 6900 and 58 u midgets.

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